Define Sn(t) = Sn(Xn − t1n) as in after XXXXXXXXXXShow that (a) sign(Xi − t) is nonincreasing in t ∈ R1, (b) R + ni(t) is nonincreasing in t when Xi > t and is nondecreasing in t when Xi hence, Sn(t)...

Define Sn(t) = Sn(Xn − t1n) as in after (3.76). Show that

(a) sign(Xi − t) is nonincreasing in t ∈ R1,

(b) R + ni(t) is nonincreasing in t when Xi > t and is nondecreasing in t when Xi

hence, Sn(t) is nonincreasing in t ∈ R1. For the particular case of an(k) = 1 ∀1 ≤ k ≤ n, (3.74) leads to the same result for the sign statistic.